Properties

Label 227850io
Number of curves $1$
Conductor $227850$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("io1")
 
E.isogeny_class()
 

Elliptic curves in class 227850io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227850.k1 227850io1 \([1, 1, 0, -212650, 38684500]\) \(-1389015072282481/44431441920\) \(-34017822720000000\) \([]\) \(2193408\) \(1.9480\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 227850io1 has rank \(1\).

Complex multiplication

The elliptic curves in class 227850io do not have complex multiplication.

Modular form 227850.2.a.io

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} - 2 q^{13} + q^{16} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display